Bai Zhenguo
School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi 710071, China.
Math Biosci Eng. 2015 Jun;12(3):555-64. doi: 10.3934/mbe.2015.12.555.
Threshold dynamics of epidemic models in periodic environments attract more attention. But there are few papers which are concerned with the case where the infected compartments satisfy a delay differential equation. For this reason, we investigate the dynamical behavior of a periodic SIR model with delay in an infected compartment. We first introduce the basic reproduction number R0 for the model, and then show that it can act as a threshold parameter that determines the uniform persistence or extinction of the disease. Numerical simulations are performed to confirm the analytical results and illustrate the dependence of R0 on the seasonality and the latent period.
周期性环境中流行病模型的阈值动态吸引了更多关注。但很少有论文涉及感染 compartment 满足延迟微分方程的情况。因此，我们研究了感染 compartment 具有延迟的周期性 SIR 模型的动力学行为。我们首先引入该模型的基本再生数(R_0)，然后表明它可以作为一个阈值参数，决定疾病的一致持续存在或灭绝。进行了数值模拟以证实分析结果，并说明(R_0)对季节性和潜伏期的依赖性。
